Apothecaries (druggists) use the following set of measures in the English system:

- 20 grains ap = 1 scruple (exact)
- 3 scruples = 1 dram ap (exact)
- 8 drams ap = 1 oz ap (exact)
- 1 dram ap = 3.888 g

An aspirin tablet contains [tex]5.00 \times 10^2 \text{ mg}[/tex] of active ingredient.

What mass in grains ap of active ingredient does it contain?

What mass in scruples?

The active ingredient in the aspirin tablet is 2.572 grains. When we further convert it to the apothecaries' system, it is approximately 0.1286 scruples.

Explanation:

To solve this problem, we first need to convert the given mass of the active ingredient in the aspirin tablet from milligrams (mg) to grams (g) since we have the conversion from dram to grams. We know that 1 gram (g) is equal to 1000 milligrams (mg), so 5.00×102 mg is equal to 0.5 g.

Announcing the next step, we convert grams (g) to drams (dr). We know that 1 drams (dr) is equivalent to 3.888 grams (g), so 0.5 g is equal to 0.5 / 3.888 dr = 0.1286 dr.

Next, we convert drams (dr) to grains (gr). As given, 1 dr is equal to 20 grains (gr), so 0.1286 dr is equal to 0.1286 * 20 gr = 2.572 gr.

Finally, to find the mass in scruples, we convert the grains (gr) to scruples (s). As given, 1 scruple is equivalent to 20 grains, so 2.572 grains is equal to 2.572 / 20 scruples = 0.1286 scruples.

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